1. MBLEDHJA DHE ZBRITJA E
POLINOMEVE
Tefik Rika

2. Tefik Rika
Identifikimi i polinomit dhe shkalla e tijë
Polinomi Emri Shkalla
monom konstant
binom linear
binom linear
binom katror
trinom katror
trinom kubik
binom kubik
12
8x – 5
4x + 3
x2 + 6
3x2 + 6x + 5
x3 + 2x – 2
x3 + 4

3. Tefik Rika
Forma standarde e polinomit:Rradhitja
sipas shkallës,duke filluar prej shkallës më të
lartë.
Polinomi Forma standarde
7 + 2x2 2x2 + 7
x3 + 6x2
9 + x – 4x2
a + a2 + a3 + 1 a3 + a2 + a + 1
– m3 – 3m2 + 2m + 8
6x2 + x3
-4x2 + x + 9
8 – 3m2 – m3 + 2m

4. Mbledhja e polinomeve:
Forma horizontale:
(x2 + 2x + 5) + (3x2 + x + 12)=
= 4x2+ 3x + 17
Forma vertikale:
x2+ 2x + 5
+ 3x2 + x + 12
= 4x2+ 3x + 17
Tefik Rika

5. Shembull:
x2 + x + 1
+ 2x2 + 3x + 2
3x2+ 4x + 3
(4b2 + 2b + 1)
+ (7b2 + b – 3)
11b2 + 3b – 2
3x2 – 4x + 8
+ 2x2 – 7x – 5
5x2 – 11x + 3
a2 + 8a – 5
+ 3a2 + 2a – 7
4a2 + 10a – 12
Tefik Rika

6. Shembull:
7d2 + 7d
+ 2d2 + 3d
9d2+ 10d
(2x2 – 3x + 5)
+ (4x2 + 7x – 2)
6x2+ 4x + 3
z2 + 5z + 4
+ 2z2 - 5
3z2 + 5z – 1
(a2 + 6a – 4)
+ (8a2 – 8a)
9a2 – 2a – 4
Tefik Rika

7. 9.1 Adding and Subtracting Polynomials
Shembull:
3d2 + 5d – 1
+ (–4d2 – 5d + 2)
–d2+ 1
(3x2 + 5x)
+ (4 – 6x – 2x2)
x2 – x + 4
7p2 + 5
+ (–5p2 – 2p + 3)
2p2 – 2p + 8
(x3 + x2 + 7)
+ (2x2 + 3x – 8)
x3 + 3x2 + 3x – 1
Tefik Rika

8. 9.1 Adding and Subtracting Polynomials
Shembull:
2x3 + x2 – 4
+ 3x2 – 9x + 7
2x3 + 4x2 – 9x + 3
5y2 – 3y + 8
+ 4y3 – 9
4y3 + 5y2 – 3y – 1
4p2 + 5p
+ (-2p + p + 7)
4p2 + 4p + 7
(8cd – 3d + 4c)
+ (-6 + 2cd – 4d)
4c – 7d + 10cd – 6
Tefik Rika

9. Shembull:
(12y3 + y2 – 8y + 3) + (6y3 – 13y +5)=
= 18y3+ y2 – 21y + 8
(7y3 + 2y2 – 5y + 9) + (y3 – y2 + y – 6)=
= 8y3 + y2 – 4y + 3
(6x5 + 3x3 – 7x – 8) + (4x4 – 2x2 + 9)=
= 6x5+ 4x4 + 3x3 – 2x2 – 7x + 1
Tefik Rika

10. Ndryshimi i polinomeve
(Vërejtje: Ja shtojmë polinomin e kundërt)
(5x2 + 10x + 2) – (x2 – 3x + 12)=
=(5x2 + 10x + 2) + (–x2) + (3x) + (–12)=
= 4x2+ 13x – 10
5x2 + 10x + 2
4x2+ 13x – 10
–(x2 – 3x + 12)
= 5x2 + 10x + 2
= –x2 + 3x – 12
Tefik Rika

11. (3x2 – 2x + 8) – (x2 – 4)=
=3x2 – 2x + 8 + (–x2) + 4=
= 2x2 – 2x + 12
(10z2 + 6z + 5) – (z2 – 8z + 7)=
=10z2 + 6z + 5 + (–z2) + 8z + (–7)=
= 9z2 + 14z – 2
Tefik Rika

12. Shembull:
7a2 – 2a
– (5a2 + 3a)
2a2 – 5a
4x2 + 3x + 2
– (2x2 – 3x – 7)
2x2 + 6x + 9
3x2 – 7x + 5
– (x2 + 4x + 7)
2x2 – 11x – 2
7x2 – x + 3
– (3x2 – x – 7)
4x2 + 10
Tefik Rika

13. Shembull:
3x2 – 2x + 10
– (2x2 + 4x – 6)
x2 – 6x + 16
3x2 – 5x + 3
– (2x2 – x – 4)
x2 – 4x + 7
2x2 + 5x
– (x2 – 3)
x2 + 5x + 3
4x2 – x + 6
– (3x2 – 4)
x2 – x + 10
Tefik Rika

14. Shembull:
(4x5 + 3x3 – 3x – 5) – (– 2x3 + 3x2 + x + 5)=
= 4x5 + 5x3 – 3x2 – 4x – 10
(4d4 – 2d2 + 2d + 8) – (5d3 + 7d2 – 3d – 9)=
= 4d4 – 5d3 – 9d2 + 5d + 17
(a2 + ab – 3b2) – (b2 + 4a2 – ab)=
= –3a2 + 2ab – 4b2
Tefik Rika

15. 9.1 Adding and Subtracting Polynomials
Cakto perimetrin e figurave:
2x2 B
x2 + x
6c + 3
c2 + 1
A
4c2 + 2c + 5
B = 6x2 + 2x
A = 5c2 + 8c + 9
2x2
x2 + x
Tefik Rika

16. Tefik Rika
Cakto perimetrin e figurave:
3x2 – 5 x
x2 + 7
C
2d2 + d – 4
D
d2 + 7
3d2 – 5d
3d2 – 5d
C = 8x2 – 10x + 14 D = 9d2 – 9d + 3

17. Cakto perimetrin e figurave:
x2 + 3 F
a + 1
a3 + 2a
E
2a3 + a + 3
F = 8x2 – 10x + 6
E = 3a3 + 4a + 4
3x2 – 5x
Tefik Rika